Swarms are actually groups of thousands of tiny creatures. The swarm automatically damages any creature sharing its space.
Creatures with the Improved Grab ability can automatically grapple enemies they strike with normal attacks. The best example of this trope would probably be the Choker, a humanoid-shaped creature about three feet tall with arms that stretch out to about ten feet long and which likes to hang out on cave ceilings.
Though certain oozes and a few other similar creatures take it even farther and engulf their victims entirely. Possibly one of the worst offenders is the Flesh Jelly. Why? Well as an ooze made of putrid flesh, being engulfed by it doesn't result in an acid bath as with most oozes, which can be magically avoided. Instead you either take damage from the convulsions of the mushy remains of previous victims and are exposed to disease, or are instantly converted into mush yourself, which so thoroughly destroys your remains that only the most potent magics in the game can bring you back.
A few creatures have possession-related abilities. Most, like ghosts, are incorporeal, but a few, like the tsochari (or the hellwasp swarm, to combine examples), are simply small enough to fit inside creatures the size of the player characters.
Pictured above is the Mega Chopper from Sonic 3 & Knuckles. In Hydrocity Zone, these little red piranha-like Mecha-Mooks swim around in certain underwater sections, and can even jump out of the water at you. If they make contact with your character, they latch on and start chewing, eating away one ring per second.
Now, almost every other harmful thing in the game either takes away all your rings or instantly kills you; by comparison, the Mega Chopper seems rather non-threatening. What truly makes this enemy dangerous is the fact that, while it's biting away, your character is unable to jump, duck, or roll. If you're underwater at the time, you're not going to be able to get back to the surface before drowning. If you get hit by an enemy while you're being Mega Chopped, you'll die one second later due to running out of rings.
There are three ways to escape a Mega Chopper. One is to enter a tube, forcing your character into a spin. Or, if you're playing co-op with Sonic and Tails, you can use Tails to jump into the Mega Chopper, provided he's not being Mega Chopped as well. Neither of these solutions are sure to be available when you need them, but fortunately, the third solution always works: randomly mash buttons on the controller until the Mega Chopper falls off. (There is no indication that flailing about might have any effect.)
In most arcade beat-em-up games, especially the plethora of licensed ones made by Konami in the 1990s (like Teenage Mutant Ninja Turtles and The Simpsons), enemies would try to grab you so other foes could beat you up, and you were instructed to "Push Buttons Wiggle Joystick" to break free.
All three of the Streets of Rage games had enemies that could grab you from behind, but in the first and third games, you could get rid of them with a shoulder throw.
Banjo-Tooie had these sort of sentient toxic fume clouds that would cling on to you and rapidly start depleting your air meter. They spawned after you killed another enemy, a sentient toxic waste barrel. Yeah, all the enemies in the game are more or less like that.
They did this with attack dogs, and it was instant death if you didn't kill them quickly enough once they latched onto you.
The Banzai chargers in World At War serve the same purpose; if you fail to kill him in time, your blood-crazed Japanese attacker will instantly bayonet you to death. And, once again, your teammates seem to have no trouble shooting them off.
MW3's survival mode has two types of dogs: normal attack dogs, and attack dogs with C4 strapped to them.
Imps are a particularly annoying version, latching on and controlling you until you shake them off.
Some of the enemies in Gunstar Heroes would sneak up behind your character and grab you in a headlock. Luckily, you could throw them off, and give them a nice shot to the face for their trouble.
In Dead Rising this is pretty much the only way that the zombies attack.
There are tiny Necromorphs in Dead Space that will often swarm you if you let them, which usually doesn't end well. Some of the bigger ones will also latch onto you until you free yourself (especially the fetal Lurker types). In addition, you're sometimes grabbed by gigantic tentacles and must shoot the weak spot while being dragged down a hallway before it'll let go.
Not to mention the Hive Mind at the end of the game. Though in that case it's more like you're the personal space invader with the fusion cutter.
Not to mention the Protozoid Slimers in Duke Nukem 3 D. How can you shoot off a creature that latches to your face with, say, a shotgun—or somehow kick it off your face—is anyone's guess.
The zombies in Eternal Darkness, though the Chatturgha and the Mantorok zombies are the ones that mostly do it.
Also the Bonethieves, which are even worse due to a particularly disturbing One-Hit Kill attack. They jump on your chest and attempt to rip your face off, tearing hunks of blood and flesh as they burrow into your body.
In F.E.A.R. 2: Project Origin, Alma repeatedly assaults Becket in close quarters, grabbing onto him and forcing Becket to fight her off.
She has a good reason too, to rape you.
Some wall-crawling enemies grab you for a quick-time event struggle too, though probably not for the same reason as Alma. I hope.
There's also an up-close and personal tug of war over a shotgun at one point. Amusingly, you have to both struggle over where its pointed, AND pull the trigger, in a slight departure from the traditional divorce between gameplay controls and Action Commands.
In the Kingdom Hearts series, Ansem/Xehanort's Heartless guardian is prone to doing this. In the first game, it can possess Sora, and will occasionally replace the Attack command with one that causes it to emerge and hold him in place. In Birth by Sleep, it'll erupt out of the ground to try to grab you and perform a piledriver, and will also dash forward and try to hold you in place so his master can get some free hits in on you. In the same game, Xehanort himself isn't exempt from it, as he'll occasionally teleport up to Terra and try to grab him by the face to unleash a Blizzaga spell at point blank range, though you can escape before you get frozen.
Justified in Kung Fu Master; the enemy Mooks were called 'Grapplers'. Granted, all they were animated doing was hugging Thomas; apparently it was the submission-hold variant of a tender embrace.
Hunters and Smokers from Left 4 Dead. For a bonus, once they have "got" you, there is no way to get out of this alone. Although if you're lucky, once a Smoker grabs you, you have about two seconds to kill it before you're helpless. Unfortunately, the Smoker's tongue ability is made all the worse by the fact that, if for some reason it can't drag you to it, it will catch you to the nearest obstacle and continue to kill you, making it all the more difficult for your allies to find it in time.
However, you can free Smoker-held allies by smacking them with your gun; this forces the Smoker to release them, so it is not actually necessary to kill the Smoker to save your teammate.
Hunters, on the other hand, can be unintentionally hilarious if you're good enough. Two achievements emphasize this: one is awarded for punching a hunter in the face as it's about to leap on you (and, if you're really good, can be repeated ad nauseam until you kill it), and another is awarded for killing a Hunter mid-leap, which will always (unless you're using a handgun) send it flying for many yards, spawning the disturbing (and not officially recognized) mini-game Hunter Punter.
You can save yourself from a Hunter after you get pounced, but you must either: Make sure you've set off a timed explosive nearby OR have set the Hunter on fire and hopes he burns out before you die.
Witches and Tanks, by contrast, love to get in your personal space to mess you up. And they will. A lot. Ironically, Witches are usually provoked if you get too close to them.
Also, in Left 4 Dead 2, the Jockey, who grabs onto your back and does his best to steer you around while you fight him and your buddies shoot at him. This is lampshaded by the characters who says "That is just wrong". This also makes them Headhumpers.
In fact every infected minus the Spitter is a personal space invader since they lack any sort of long range weaponry and insist on beating you to death with their fists (or lack thereof). The Charger will stalk and eventually slam himself straight through a group of survivors, carrying the first he hits (and scatters the others) several yards and continuously slam them into the ground, ceiling and walls until he or his victim are killed.
The pile of evil pancakes known as a "Like-Like" appear in several games. They are notable mainly due to their nasty habit of eating your equipment.
Then there were the Wall Masters and Floor Masters. If these giant hands land on your head they carry you back to the beginning of the dungeon and you have to re-do all that trekking to get back to where you were before. In OoT Link does struggle rather graphically as it slowly drags him by the head up into the darkness above.
Another enemy in The Legend of Zelda: Ocarina of Time are The Dead Hands in the Well and the Shadow Temple. It's basically a set of six skeletal arms reaching out of the earth trying to grab your head. And if one did, you then had to deal with a burrowing, long-necked, bloodstained, jaw-unhinging zombie that would slowly slither up to you and try to take a chomp out of your face.
SMG2 introduces the Smeech, a little pig-like enemy with wings and huge lips. If Mario approaches it alone, it will avoid him. If approached while riding Yoshi, it will fly towards him and fiercely kiss him on the lips, which blocks his ability to eat enemies
In Metal Gear Solid 3 Snake Eater, if Snake swim/wades in the jungle waters for too long, leeches may attach themselves to his skin and drain his stamina. You can burn them off with a cigar.
The eponymous monsters in the Metroid series. You get a really good look at their undercarriage when they latch onto you in the Metroid Prime games. Or at least you do until their life-sucking causes static snow to fill your visor and you start panicking.
Also in Corruption, Gandrayda will do this when you fight her.
In Super Metroid there's also these flea/tick-like bugs that latch on to Samus and start draining her health.
The zombies and the Ganados in the Resident Evil series, but Las Plagas are the most blatant space invaders.
Resistance: Fall of Man had "menials" which latched onto your face and screamed at you and tore you apart. It's an FPS, so... scary stuff.
Star Wars Episode III: Revenge of the Sith, the video game, GBA and NDS versions has strangling droids, and clone troopers that shoot strangling string lasers.
The Fuzzies and stronger types of Swoopers from the Paper Mario games. Some will just hit you once, while others require button mashing to get them off. The Zap Tap badge keeps them off you entirely in either case.
Ty the Tasmanian Tiger has leeches and ticks, who can take off a sizable portion of your life if not shaken off quickly. If it wasn't for the the fact that you can only take four hits at first, and they're so low to the ground only your exploding boomerangs can take them out without precision aiming, they wouldn't be a threat.
The PS2 game War Of The Monsters gives a giant preying mantis the power to fire a flying leech.
Critters from the classic Xenophobe were fond of crawling on your space marine, alien, or duck (Yes, duck) and chewing off life. A simple button press solved the issue, though.
Almost ubiquitous in the Silent Hill series, with each game possessing at least one variant. Perhaps the worst, both in terms of gameplay and sheer mindfuckery, are either the Doorman/Abstract Daddy monsters in the second game, which are massive and proceed to swallow the player character's head, or the Slurpers in the third game that knock the (teenaged, female) player character to the ground and climb on top of her in preparation for "fun time".
If you get too close to an unarmed enemy in Condemned: Criminal Origins, he'll leap on you and start headbutting you to death.
The moles in Mario Kart would jump out of the ground onto your kart. They would slow you down and block your view until you threw them off.
Invading the player character's personal space and grabbing on to them is a popular attack for the ghosts in the Fatal Frame series. For a couple of the bosses, being touched is also a One-Hit Kill.
Gets done occasionally in World Of Warcraft, particularly by any mob that uses the Death Grip ability to pull players into melee range.
A particularly nasty case of this is exemplified by the first boss in the Trial of the Crusader raid dungeon, Gormok the Impaler, who carries around a stable of Snobolds with him that he throws at players during the encounter. These creatures are incredibly annoying as they damage, stun, and interrupt their target, can't be attacked by their target, and can only be killed with direct damage, not AoE. For added hilarity, there's an achievement for doing the entire boss encounter without killing the Snobolds.
The very next major boss, Lord Jaraxxus, periodically summons demon minions to aid him. One of these, the Mistress of Pain, likes to leap at players, grab them, and do a spinning pile driver move reminiscent of Zangief from Street Fighter.
Valkyr Shadowguards in phase 3 of the Lich King encounter in Icecrown Citadel fly to their target players, pick them up, and drop them over the side of the Frozen Throne platform, for a guaranteed death if they aren't killed first.
Light bugs in Limbo attach themselves on the protagonist, forcing him to perpetually walk in one direction, only stopping when he hits an obstacle and only turning around when he steps into a beam of light. Fortunately, the boy isn't the only one which the limbo wants to see eaten.
Loco Roco has Kojas, a small variation of your average enemies which attach themselves upon the locoroco, making it harder to jump. Their weakness - Water
Batman Arkham Asylum has escaped lunatic inmates who lunge and grapple you until you shake them off.
Amorphous has Clutters, which bombard you with their spawn that latches onto you, slowing you as more become attached. If you let enough of the baby Clutters latch onto you they stun you for a while, leaving you completely open to all attacks.
Nethack monsters that do this are some of the most dangerous in the game. If a kraken or giant eel grabs you, then no matter how big and strong you are, you have at most one round to get free before it drowns you.
Bone Leeches, Thieves and Hands in Blood. Pretty hard to get off once they latch on to you, and that would just put them back in the exact same point where they were the moment before they jumped at you, so they'd just jump back in the fracture of a second, prompting you to shoot in every direction like a maniac and probably run out of ammo in the process. Not helped by the fact that while you're doing this, the entire HUD (and most of the screen) is obscured by those REALLY ugly critters. The best solution is really to save the moment you hear them coming than, blast everything with napalm.
In Oddworld: Stranger's Wrath, various ammo types such as Fuzzles will invade the personal space... of enemies! Played straight with Sekto though, who is an Oktigi, a octopus-like creature that latches onto the head of something and then proceeds to control them. In Sekto's case, he latched onto the previous Guardian Steef.
The second stage of Drol had magnets that would latch onto you. They weren't directly harmful, but prevented you from firing in one direction until you shook them loose by moving down or up a hatch.
In Mass Effect 3, Husks gain this ability. They can grab the player, forcing you to mash buttons in order to escape their grip. There's also the Banshee, the warped Reaper version of an Asari. If she's not blasting you from afar, she's right in your face, preparing to plunge her claws into your chest.
In Super Smash Bros. Brawl's Subspace Emissary mode, the Bucculus likes to hide under ground, then leap out at careless players and latch on tight. They make a loud smooching sound as the sac attached to their lips fills up and you take damage, then, once you finally pry them off, they bounce around before hiding back under ground to start the process all over again.
The Combat Tentacles with the spike on the tip in Ecco The Dolphin, which latch on and stay there for a while. Made frustrating by the fact that you're underwater and only have so much time to shake them before you drown. (hint: Usually getting loose requires a lot of charging, aka mashing the B button.)
The Walkers in Dead Island. They will frequently be laying on the ground, visually indistinguishable from a corpse. If you walk over them, they will spring up and grapple you. Safest thing to do when not actively fighting zombies is to kick every corpse you pass to make sure its a corpse and not a walker. Keep in mind that Walkers are the least dangerous of the various zombies. God help you if you get grappled like this while Infected are coming.
Saints Row The Third has this during the Zombie Attack mission. If you get grabbed by a zombie you have to frantically pound a button to get it (and the others that accumulate since you can't move) off.
Okami has the "Dead Fish" enemies, which, when brought below half health, like to glomp onto Ammy and explode.
MechWarrior Living Legends features the Battlearmor, which are very small, very agile (and verydeadly) jump-jet equipped suits that the players can use. The most effective tactic for a battlearmor player is to get as close to an enemy BattleMech as possible, and run around in circles under their feet while carving off their legs. More skilled battlearmor players rely on jumping onto the enemy's head, where the enemy cannot shoot them. The battlearmor then can blast through the cockpit glass and kill the pilot at their leisure, or start hacking off their arms. The pilot of the mech will be almost totally helpless - he will have to rely on allies shooting off the battlearmor, or firing his splash damage weapons at point blank. The aforementioned method is often used by battlearmor to bait the enemy's buddies into shooting the mech.